The Tower of Hanoi puzzle is an engaging and challenging problem for middle school students and an application of exponential functions. It also is the setting for an elegant proof by mathematical induction that the minimum number of moves M to move n disks from one disk to another is given by M = 2^n - 1.

Here is a Java implementation of the same puzzle.
http://nlvm.usu.edu/en/nav/frames_asid_118_g_3_t_2.html?open=instruction...